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Abstract

Effective learning planning requires information on the obstacles to learning a given concept that students experience to create a learning flow that matches the students’ characters, including in the learning of the concepts of relations and functions. The research aims to determine the learning obstacles (LOs) that students experience in learning the concepts of relations and functions as per the criteria of the theory of didactic situations (TDS). Employing the case study method, this qualitative research was conducted with subjects that included 19 prospective teacher students who had taken a diagnostic test and participated in in-depth interviews. An analysis was conducted based on three TDS criteria, namely action, formulation, and validation. The results revealed two types of LOs that students experienced in learning the concepts of relations and functions: 1) ontogenic obstacles and 2) epistemological obstacles. The first type of obstacles included 1a) the inability to properly understand the definition of the intersection of two relations, referred to as conceptual ontogenic obstacle, and 1b) the inability to relate the concept of relations in drawing a Hasse diagram, referred to as instrumental ontogenic obstacle. Meanwhile, the second type included 2a) the difficulty in expressing relations in the forms of mapping diagrams and graphs, 2b) the difficulty in determining the range of ​​a function, 2c) the difficulty in identifying relations which are also functions, 2d) the inability to represent relations in the forms of mapping diagrams, and 2e) the inability to write a function as a set of ordered pairs. It is recommended that these LO findings be taken into consideration in designing learning tools.

Keywords

Learning Obstacle Diagnostic Test Relations and Functions Ontogenic Obstacle Epistemological Obstacle

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How to Cite
Kesumawati, N., Lusiana, Fuadiah, N. F., & Retta, A. M. (2024). Obstacles to Relations and Functions Concepts Learning in Terms of Theory of Didactic Situations Criteria. Jurnal Pendidikan Matematika, 18(2), 259–272. https://doi.org/10.22342/jpm.v18i2.pp259-272
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References

  1. Abdussamad, Z. (2021). Qualitative Research Methods [in Bahasa]. Syakir Media Press.
  2. Adelia, M., Noerruddin, A., & Kholidah, N. R. J. (2023). Analysis of Students' Mathematical Communication Skills on Relationships and Functions in Terms of Gender Differences in Class VIII of Smpn 2 Parengan, Tuban Regency [in Bahasa]. Jurnal Edumatic : Jurnal Pendidikan Matematika, 4(2), 54–67. https://doi.org/10.21137/edumatic.v4i2.806
  3. Akçakin, V. (2018). Teaching mathematical functions using geometric functions approach and its effect on ninth grade students’ motivation. International Journal of Instruction, 11(1), 17–32. https://doi.org/10.12973/iji.2018.1112a
  4. Ats-Tsauri, M. S., Cholily, Y. M., Azmi, R. D., & Kusgiarohmah, P. A. (2021). Relationship and Function Module Based on Mathematical Communication Skills [in Bahasa]. JNPM (Jurnal Nasional Pendidikan Matematika), 5(1), 109. https://doi.org/10.33603/jnpm.v5i1.3569
  5. Aziiza, Y. F., Rosjanuardi, R., & Juandi, D. (2022). Didactic Design of the Concept of Surface Area of Flat-Sided Prism Based on van Hiele’s Theory in Online Learning. Jurnal Pendidikan Matematika, 16(1), 73–88. https://doi.org/10.22342/jpm.16.1.13789.73-88
  6. Bardini, C., Pierce, R., Vincent, J., & King, D. (2014). Undergraduate mathematics students’ understanding of the concept of function. Journal on Mathematics Education, 5(2), 85–107. https://doi.org/10.22342/jme.5.2.1495.85-107
  7. Cahyani, L. (2019). Analysis of Discrete Mathematics Learning Difficulties in Students [in Bahasa]. Proceedings of the National Seminar on Postgraduate Education Program at PGRI University, Palembang, 430–442.
  8. Cheah, C. S. (2020). Factors contributing to the difficulties in teaching and learning of computer programming: A literature review. Contemporary Educational Technology, 12(2), 1–14. https://doi.org/10.30935/cedtech/8247
  9. Clem, A. L., Rudasill, K. M., Hirvonen, R., Aunola, K., & Kiuru, N. (2021). The roles of teacher–student relationship quality and self-concept of ability in adolescents’ achievement emotions: temperament as a moderator. European Journal of Psychology of Education, 36(2), 263–286. https://doi.org/10.1007/s10212-020-00473-6
  10. Fitrianna, A. Y., & Rosjanuardi, R. (2021). Identification of Junior High School Students’ Error Types in Understanding Concept About Relation and Function. Infinity Journal, 10(2), 175–190. https://doi.org/10.22460/infinity.v10i2.p175-190
  11. Isnawan, M. G. (2023). Didactical Design Research (Ddr) as an alternative research design in preparing didactical designs [in Bahasa]. October 2022.
  12. Greefrath, G., Siller, H. S., Vorhölter, K., & Kaiser, G. (2022). Mathematical modelling and discrete mathematics: opportunities for modern mathematics teaching. ZDM - Mathematics Education, 54(4), 865–879. https://doi.org/10.1007/s11858-022-01339-5
  13. Hajar, Y., Suryadi, D., & Usdiyana, D. (2023). Learning Obstacles of Islamic Junior High School Students on Angle Concepts. International Journal of STEM Education for Sustainability, 3(2), 268–285. https://doi.org/10.53889/ijses.v3i2.236
  14. Handayani, N. W. P., Ardana, I. M., & Sudiarta, I. G. P. (2020). Learning Media Based on the Bruner Model, Local Culture, and Scaffolding to Improve Understanding of Relationship and Function Concepts [in Bahasa]. JNPM (Jurnal Nasional Pendidikan Matematika), 4(2), 221. https://doi.org/10.33603/jnpm.v4i2.3235
  15. Hutagaol, Rejeki, A. S., Yopita, & Andau, V. (2022). Analysis of Students' Difficulties in Solving Story Problems on Relationship and Function Material [in Bahasa]. Jurnal Pendidikan Matematika Undiksha, 4(1), 491–498. https://doi.org/10.23887/jjpm.v13i1.45909
  16. Janan, T., & Hanafi, A. R. B. (2022). Analysis of Student Errors in Solving Equations and Inequalities Questions in Calculus I Course [in Bahasa]. Jurnal Pendidikan Sains Dan Komputer, 2(01), 8–20. https://doi.org/10.47709/jpsk.v2i01.1331
  17. Kandaga, T., Rosjanuardi, R., & Juandi, D. (2022). Epistemological Obstacle in Transformation Geometry Based on van Hiele’s Level. Eurasia Journal of Mathematics, Science and Technology Education, 18(4). https://doi.org/10.29333/ejmste/11914
  18. Kartika, M., & Hiltrimartin, C. (2019). Application of the Eliciting Activities (MEAs) Model in Learning Mathematics on Relationships and Functions [in Bahasa]. Jurnal Gantang, 4(2), 161–168. https://doi.org/10.31629/jg.v4i2.1347
  19. Khan, M. B., Santos-García, G., Noor, M. A., & Soliman, M. S. (2022). Some new concepts related to fuzzy fractional calculus for up and down convex fuzzy-number valued functions and inequalities. Chaos, Solitons and Fractals, 164(September), 112692. https://doi.org/10.1016/j.chaos.2022.112692
  20. Larson, N., & Pettersson, K. (2017). A study of students ’ concept images of inverse functions in. 22, 85–102.
  21. Maatuk, A. M., Elberkawi, E. K., Aljawarneh, S., Rashaideh, H., & Alharbi, H. (2022). The COVID-19 pandemic and E-learning: challenges and opportunities from the perspective of students and instructors. Journal of Computing in Higher Education, 34(1), 21–38. https://doi.org/10.1007/s12528-021-09274-2
  22. McCulloch, A. W., Lovett, J. N., & Edgington, C. (2017). Developing preservice teachers’ understanding of function using a vending machine metaphor applet. Proceedings of the 39th Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education, 1281–1289.
  23. Miftah, R., Amalina, A. N., & Kurniawati, L. (2022). Didactical design of mathematical reasoning on three dimensional in high school. Journal of Physics: Conference Series, 2157(1). https://doi.org/10.1088/1742-6596/2157/1/012043
  24. Natalia, S., Darhim, Kusumah, Y. S., & Ditasona, C. (2023). Learning Obstacle to Ontogeny of Mathematics Teacher Candidates on Number Theory. Journal of Education Research and Evaluation, 7(3), 51–525. https://doi.org/10.23887/jere.v7i3.66629
  25. Noto, M. S., Pramuditya, S. A., & Fiqri, Y. M. (2018). Design of Learning Materials on Limit Function Based Mathematical Understanding. Infinity Journal, 7(1), 61. https://doi.org/10.22460/infinity.v7i1.p61-68
  26. Pinheiro, A. L. V., Rachelli, J., & Porta, L. D. (2022). Study of Round Bodies: Conceptions and Praxis of a Didactic Sequence in Light of Guy Brousseau’s Theory. Acta Scientiae, 24(6), 634–665. https://doi.org/10.17648/acta.scientiae.7402
  27. Prabowo, A., Suryadi, D., Dasari, D., Juandi, D., & Junaedi, I. (2022). Learning Obstacles in the Making of Lesson Plans by Prospective Mathematics Teacher Students. Education Research International, 2022. https://doi.org/10.1155/2022/2896860
  28. Puspita, E., Suryadi, D., & Rosjanuardi, R. (2023). Learning Obstacles of Prospective Mathematics Teachers : A Case Study on the Topic of Implicit Derivatives. 14(1), 174–189.
  29. Raharjo, A. M., & Christanti, A. D. I. (2020). Analysis of Class VIII Students of SMP Kanisius Gayam Mistakes in Solving Relationship and Function Questions [in Bahasa]. National Mathematics Education Seminar, 1(1), 281–292.
  30. Rahmi, L., & Yulianti, K. (2022). Learning Obstacles Faced by Students in Understanding Relationship and Function Topics [in Bahasa]. Jurnal Pembelajaran Matematika Inovatif, 5(4), 929–940. https://doi.org/10.22460/jpmi.v5i4.929-940
  31. Rayhan, N. C., & Juandi, D. (2023). Students Learning Obstacles Related to Mathematical Literacy Problem: A Systematic Literature Review. Mathline : Jurnal Matematika Dan Pendidikan Matematika, 8(2), 457–472.
  32. Restianim, V., Pendy, A., & Merdja, J. (2020). Flores University Mathematics Education Students' Learning Styles in Understanding Function Concepts [in Bahasa]. Science, and Physics Education Journal (SPEJ), 3(2), 48–56. https://doi.org/10.31539/spej.v3i1.990
  33. Ria, A. M., Lusiana, L., & Fuadiah, N. F. (2023). Didactical Design of Algebraic Function Limit Material in High School Mathematics Learning [in Bahasa]. Jurnal Cendekia : Jurnal Pendidikan Matematika, 7(1), 862–873. https://doi.org/10.31004/cendekia.v7i1.2189
  34. Sandefur, J., Lockwood, E., Hart, E., & Greefrath, G. (2022). Teaching and learning discrete mathematics. ZDM - Mathematics Education, 54(4), 753–775. https://doi.org/10.1007/s11858-022-01399-7
  35. Santiago, P. V. da S., Darmayanti, R., & Sugianto, R. (2023). Conquering IMO Problems in Brazil by Recognizing the Didactic Situation, Mathematics Teachers Must Know! Assyfa Learning Journal, 1(2), 73–90. https://doi.org/10.61650/alj.v1i2.60
  36. Sari, A. D., Suryadi, D., & Dasari, D. (2023). Learning obstacle of probability learning based on the probabilistic thinking level. Journal on Mathematics Education, 15(1), 207–226. https://doi.org/10.22342/jme.v15i1.pp207-226
  37. Setiyani, Putri, D. P., Ferdianto, F., & Fauji, S. H. (2020). Designing a digital teaching module based on mathematical communication in relation and function. Journal on Mathematics Education, 11(2), 223–236. https://doi.org/10.22342/jme.11.2.7320.223-236
  38. Sidik, G. S., Suryadi, D., & Turmudi, T. (2021). Learning Obstacle on Addition and Subtraction of Primary School Students: Analysis of Algebraic Thinking. Education Research International, 2021. https://doi.org/10.1155/2021/5935179
  39. Suryadi, D. (2018). Didactical Design Research (DDR) and its Implementation [in Bahasa]. Gapura Press.
  40. Umah, U. (2016). Developing Students' Reasoning in Learning Function Concepts [in Bahasa]. Proceedings of the National Seminar on Mathematics Education, September, 796–805.
  41. Utami, N. S., Aswin, Riastuti, A., Sutomo, W. A. B., Khariunnisa, Kurniati, N., Armania, P., & Jupri, A. (2023). Learning Algebraic Forms Based on Didactical Situation Theory for High School Students at the Graha Asuh Jabal 165 Foundation, Bandung Regency [in Bahasa]. Jurnal Pengabdian Kepada Masyarakat Indonesia (JPKMI), 3(1), 38–46. https://doi.org/10.55606/jpkmi.v3i1.1217